Linear regression with multivariate responses. Consider training data [(x{i),y(i))},-=1mm where xii) 6 Rd and y\") e le. Consider a model y = Ax, Where A E leXd is unknown. Estimate A by solving least squares linear regression (a) (b) (C) It - (i]_ (1'12 mingny Ax \"- f: 1 1 0 0 1 2 FindAinthecase oftrainingdata {[(0), 1 ],,[(1) 1 ],,[(1) 3 ]}Youmayuseacom 0 1 1 puter to perform linear algebra. Hint: the problem can be simplified by observing that each output dimension can be computed separately from the others. If you use this fact, justify it in your response. Response: Consider the case of generic training data. Let Y be the k x n matrix such that 19-,- = yr). Let X be the n x d matrix Where Xi = xffi). Provide a formula for the least squares estimate of A. Make sure to check that the matrix dimensions match in any matrix products that appear in your answer. Use the same hint as in part (a). Response: Show that any prediction under this learned model is a linear combination of the response values (32(1),. . . ,yw). That is, for the A in part (b), show that Ax E span(y{1}, .. . ,ytnl) for any x. You may assume that X is rank d